Explain the differences between computing the derivatives of functions that are defined implicitly and explicitly. Select each of the following that correctly describes the differences O A. When computing the denvative of an explicitly defined function y = f(x), the result dy / dx depends only on x When computing the derivative of an implicitly defined function, the result dy / dx depends only on y O B. When computing the derivative of an explicitly defined function y = f(x), the result dy / dx depends only on x. When computing the derivative of an implicitily defined function, the result dy /dx may depend on both x and y. O C. To compute the denivative of an explicitly defined function y = f(x), use the rules of differentiation to differentiate y with respect to x. To compute the derivative of a function defined implicitly by an equation, write the independent variable y as a function of the dependent variable and x, use the chain rule to differentiate each term of the equation with respect to x, and then solve for dy/ dx. O D. To compute the denvative of an explicitly defined function y = f(x), use the rules of differentiation to differentiate y with respect to x. To compute the derivative of any function defined implicitly by an equation, solve the equation for y and then differentiate each term of the resulting function with respect to x to find a single definition of dy / dx

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: